Grinding method

ABSTRACT

It is provided that a grinding method of a rotating workpiece W having a cylindrical part and at least one end face beside the cylindrical part. The grinding wheel  30  has a rotational axis parallel to a rotational axis of the workpiece W and has an external surface  30 FM, at least one side surface  30 SM and at least one R-part  30 KM between the external surface  30 FM and the side surface  30 DM. The grinding wheel  30  is moved backward in oblique direction to the end face to grind the end face for rough grinding in a process [ 1] . The grinding wheel is moved forward perpendicular to the rotational axis of the workpiece to grind the end face for finish grinding in a process [ 2   a ] and to grind the cylindrical part for rough grinding in a process [ 2   b].

INCORPORATION BY REFERENCE

The present application claims priority under 35 U.S.C. §119 to Japanese Patent Application No. 2007-157291, filed on Jun. 14, 2007. The contents of that application are incorporated herein by reference in their entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to a grinding method of a workpiece, for example, a crankshaft, which has an end face, and/or which has an end face and a cylindrical part.

2. Discussion of the Background

It is well-known that a conventional grinding machine which grinds cylindrical parts (pins, journals and/or etc.) and end faces (shoulder parts and/or etc.) of a crankshaft. The rotational axis of the crankshaft is parallel to the cylindrical parts and perpendicular to the end faces.

Japanese patent application publication No. 2005-324313 discloses a grinding method of the cylindrical part and the end faces. For grinding the cylindrical part and the end faces, as shown in FIGS. 1 and 2, a grinding wheel 30 is fed in oblique direction ([A1 a], [A1 b], [A1] and [A4]), then in thrust direction ([A2] and [A5]). In FIGS. 1 and 2, hatching regions with horizontal and vertical lines indicate grinding allowances ground by an R-part 30KM of the grinding wheel 30. Hatching regions with only horizontal lines are ground by parts of grinding wheel 30 except the R-part 30KM.

With referring to FIGS. 1(A) and 1(B), there will be explained grinding method of one cylindrical part and one end face. In the prior art, first process [A1] has a rough grinding step of the end face [A1 a] and a rough grinding step of the cylindrical part [A1 b], as shown in FIG. 1(A). In the step [A1 a], the grinding wheel 30 is obliquely fed to C-axis so as to remove a grinding allowance [A1 a(1)]. During the step [A1 a], the R-part 30KM of the grinding wheel 30 is used (works). Where the grinding wheel 30 is further fed to C-axis obliquely, an external surface 30FM of the grinding wheel 30 reaches the cylindrical part of the workpiece W and the step [A1 b] begins. In the step [A1 b], the grinding wheel 30 is continuously fed so that the R-part 30KM removes the grinding allowance [A1 b(1)] and the external surface 30FM removes a grinding allowance [A1 b(0)]. Thus, during the step [A1 b], the R-part 30KM and the external surface 30FM of the grinding wheel 30 are used (work).

In sequence, second process [A2] takes place as shown in FIG. 1(B). The grinding wheel 30 is fed in substantial parallel to C-axis for finish grinding of the end face. In the second process [A2], the R-part 30KM (the width of Δ1 equals to f/n of the R-part 30KM) and a side 30SM of the grinding wheel 30 are used (work) in order to remove a grinding allowance [A2(1)]. “Δ1” is depth of grinding per a revolution of a spindle (mm/rev), “f” is feeding speed (mm/min) in Z-axis direction, and “n” is revolution speed (rev/min) of the spindle. The width of Δ1 (equals to f/n of the R-part 30KM) grinds a part of the workpiece W which reaches a region A-P of the grinding wheel 30, as shown in FIG. 1(B). The side 30SM grinds a part of the workpiece W which passes through the region A-P until reaching a region B-P. In the second process [A2], finish grinding of the cylindrical part may take place. As explained, in the processes A1 and A2 of the prior art, grinding allowances [A1 a(1)], [A1 b(1)] and [A2(1)] are removed by the R-part 30KM of the grinding wheel 30.

Next, there will be explained grinding method of one cylindrical part and two end faces with referring to FIG. 2. FIG. 2 shows all processes [A1] to [A6] in order to grind the cylindrical part and the end faces which are located both sides of the cylindrical part, e.g., crankpin and crank arms of a crankshaft. In the processes [A1] and [A2], one end face is ground by substantial same processes [A1] and [A2] of FIGS. 1(A) and 1(B). In the process [A3], the grinding wheel 30 is fed without grinding. In the processes [A4] and [A5], the other end face is ground by substantial same processes [A1] and [A2] of FIGS. 1(A) and 1(B). In the process [A6], the grinding wheel 30 is fed in parallel of C-axis for finish grinding of the cylindrical part. The R-part 30KM of the grinding wheel 30 grinds the hatching regions with horizontal and vertical lines as the grinding allowances.

In the prior art, the removal amount (grinding allowances) by the R-part 30KM of the grinding wheel 30 is larger than by the other parts. Thus the grinding wheel of the prior art wears away early at the R-part 30KM so as to shorten the durability of the grinding wheel 30 relatively. Further the shape of R-part 30KM is transferred to the boundary between the cylindrical part and the end face of the workpiece. Therefore, when the R-part 30KM looses its shape because of frequency of usage, the workpiece may not obtain sufficient precision and may be defective.

SUMMARY OF THE INVENTION

According to the invention, it is provided that a grinding method of a rotating workpiece having a cylindrical part and at least one end face beside the cylindrical part. A grinding wheel has a rotational axis parallel to a rotational axis of the workpiece and has an external surface, at least one side surface and at least one R-part between the external surface and the side surface. The grinding wheel is moved backward in oblique direction to the end face to grind the end face for rough grinding by the side surface. Next, the grinding wheel is moved forward perpendicular to the rotational axis of the workpiece to grind the end face for finish grinding by the R-part and to grind the cylindrical part for rough grinding by the R-part and the external surface.

The present invention also provides a grinding method of a rotating workpiece having a cylindrical part and two end faces at both sides of the cylindrical part. A grinding wheel has a rotational axis parallel to a rotational axis of the workpiece and has an external surface, two side surfaces and two R-parts between the external surface and the side surfaces. The grinding wheel is moved backward in oblique direction to the one end face to grind the one end face for rough grinding by one of the side surfaces. Next, the grinding wheel is moved forward perpendicular to the rotational axis of the workpiece to grind the one end face for finish grinding by one of the R-parts and to grind a part of the cylindrical part close to the one end face for rough grinding by the one R-part and the external surface. Further, the grinding wheel is moved backward in oblique direction to the other end face to grind the other end face for rough grinding by the other side surface. Next, the grinding wheel is moved forward perpendicular to the rotational axis of the workpiece to grind the other end face for finish grinding by the other R-part and to grind a part of the cylindrical part close to the other end face for rough grinding by the other R-part and the external surface. Finally, the grinding wheel is moved parallel to the rotational axis of the workpiece for finish grinding of the cylindrical part by the one R-part and the external surface.

The present invention further provides a grinding method of a rotating workpiece having at least one end face. A grinding wheel has a rotational axis parallel to a rotational axis of the workpiece and has an external surface and at least one side surface. The grinding wheel is moved backward in oblique direction to the end face to grind the end face for rough grinding by the side surface. Next, the grinding wheel is moved forward perpendicular to the rotational axis of the workpiece to grind the end face for finish grinding by a boundary between the external surface and the side surface.

BRIEF DESCRIPTION OF THE DRAWINGS

Various objects, features and many of the attendant advantages of the present invention will be readily appreciated as the same becomes better understood by reference to the following detailed description of the preferred embodiments when considered in connection with the accompanying drawings, in which:

FIGS. 1(A) and 1(B) are explanatory drawings of a prior art,

FIG. 2 is an explanatory drawing of another prior art,

FIG. 3 is a plan view of a grinding machine applied to a first embodiment of the present invention,

FIG. 4 is a side view of FIG. 3,

FIG. 5 shows a grinding wheel of the grinding machine,

FIGS. 6(A) and 6(B) are explanatory drawings of the first embodiment,

FIG. 7 an explanatory drawing of a second embodiment of the invention,

FIGS. 8(A) and 8(B) show examples of a workpiece ground by the invention, and

FIG. 9 is an explanatory drawing of a third embodiment of the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

A first embodiment of a grinding method related to the present invention will be described with reference to FIGS. 3 to 6 and 8. FIG. 3 shows a schematic plan view of a grinding machine 1 which grinds a workpiece W having one or more end faces and cylindrical parts, e.g. a crankshaft. FIG. 4 shows a schematic side view of the grinding machine 1 along A-direction in FIG. 3, and FIG. 5 shows an external view and a section view of a grinding wheel 30. FIGS. 8(A) and 8(B) respectively show a crankshaft W1 and a transmission shaft W2 as examples of the workpiece W.

[Grinding Machine 1]

The grinding machine 1 comprises a base 2, a spindle table TB1, a wheel table TB2 and a computerized numerical controller (CNC) 40. The grinding wheel 30 is a disc-like and is disposed on the wheel table TB2. In detail, the grinding wheel 30 attached to a wheel drive motor 24 mounted on the wheel table TB2, and is driven by the wheel drive motor 24 about a wheel rotational axis TZ which is parallel to Z-axis. The grinding wheel 30, for example, has an iron core 30 b and a CBN grindstone 30 a surrounding the iron core 30 b. Z-axis is an axis of a ball screw 23B (described hereinafter) and is parallel to C-axis which is a rotational axis of the workpiece W. As shown in FIG. 5, the CBN grindstone 30 a of the grinding wheel 30 has external surface 30FM, side surfaces 30SM, R-parts 30KM which is a boundary between the external surface 30FM and the side surfaces 30SM, internal surfaces 30RM and back taper surfaces 30BM. Respective back taper surfaces 30BM have a predetermined angle θ. The grindstone 30 a may not have the back taper surfaces 30BM like the prior art in FIGS. 1(A) and 1(B).

A coolant nozzle 70 is a nozzle which is configured to supply coolant for lubrication of the grinding point between the workpiece W and the grinding wheel 30. The coolant is supplied to the grinding point from a coolant supply pump 74 controlled by the CNC 40 via the coolant nozzle 70. A coolant valve 72 is controlled by the CNC 40 in order to adjust the amount of coolant supply.

The wheel table TB2 is driven by a wheel table motor 22 to move along X-axis through a ball screw 22 and a nut (not shown) fixed on the wheel table TB2. X-axis is an axis of the ball screw 22 and is perpendicular to Z-axis and C-axis.

The spindle table TB1 is driven by a spindle table motor 23 to move along Z-axis through the ball screw 23B and a nut (not shown) fixed on the spindle table TB1. A tail stock 21T is fixed on the spindle table TB1. Facing the tail stock 21T on the spindle table TB1, a head stock 21D is slidably mounted in order to adjust variety of lengths of the workpieces W. A spindle motor 21 is installed into the head stock 21D and has a clamp 21C to clamp the workpiece W rotatably about C-axis. The workpiece W is held by the clamp 21C and a tail spindle 21S of the tail stock 21T therebetween. The axis connecting the clamp 21C and the tail spindle 21S is C-axis. The workpiece W is rotated by the spindle motor 21 about C-axis and is ground by the grinding wheel 30. During the grinding, an automatic sizing device (not shown) detects the size of the workpiece W.

The wheel table motor 22 has a position sensor 22E which detects the position of the wheel table TB2 along X-axis. The spindle table motor 23 has a position sensor 23E which detects the position of the spindle table TB1 along Z-axis. The spindle motor 21 has a position sensor 21E which detects the rotational angle and the rotational speed of the workpiece W. Variety of sensors is applied to the position sensors 21E, 22E and 23E, and encoders are applied to the embodiment.

The CNC 40 comprises a CPU 41, a storage 42, an input/output device 43 (keyboard, monitor, etc.), an interface 44, drive units 51-54 and etc. The CNC 40 controls the spindle motor 21, the wheel table motor 22, the spindle table motor 23 and the wheel motor 24 depending on grinding data and grinding program stored in the storage 42. The CPU 41 calculates command based on input data from the input/output device 43, the program and the data stored in the storage 42 and external input data through the interface 44, and outputs the command through the interface 44. External input data is signals of the position sensors 21E, 22E and 23E and the automatic sizing device. The command is output to the drive units 51-54 in order to control the rotational angle/speed of the workpiece W, the position of the wheel table TB2 along X-axis, the position of the spindle table TB1 along Z-axis and the rotational speed of the grinding wheel 30.

The drive unit 51 drives the spindle motor 21 which controls the rotation of the workpiece W about C-axis. The drive unit 52 drives the wheel table motor 22 which controls the position of the wheel table TB2 along X-axis. The drive unit 53 drives the spindle table motor 23 which controls the position of the spindle table TB1 along Z-axis. The drive unit 54 drives the wheel motor 24 which controls the rotation of the grinding wheel 30. The respective drive units 51-53 gain the signals of the position sensors 21E, 22E and 23E, compensate the command from the CPU 41 as feedback control, and drive the spindle motor 21, the wheel table motor 22 and the spindle table motor 23. In FIG. 3, although the wheel motor 24 has no sensor, the wheel motor 24 may have a sensor for feedback control.

[Examples of the Workpiece]

FIG. 8(A) and FIG. 8(B) show examples of the workpiece W which has the cylindrical part(s) parallel to the rotational axis (C-axis) and the end face(s) perpendicular to the rotational axis (C-axis). FIG. 8(A) shows one example, the crankshaft W1 which has plural crankpins (P1 to P4), crank journals (J1 to J5) and shoulders. FIG. 8(B) shows another example, the transmission shaft W2 which has plural cylindrical parts (E3 to E7) and shoulders.

[Grinding Method of One Cylindrical Part and One End Face Adjacent Each Other]

The grinding method of the first embodiment is applied to the workpiece W with one cylindrical part and one end face adjacent each other (e.g., journal J1 and adjacent shoulder shown in FIG. 8(A), cylindrical parts E3, E4, E6 and E7 and adjacent shoulders shown in FIG. 8(B) and/or etc.). The grinding method has a first process shown in FIG. 6(A) and a second process shown in FIG. 6(B). In FIGS. 6(A) and 6(B), hatching regions with horizontal and vertical lines indicate grinding allowances ground by the R-part 30KM of the grinding wheel 30. Hatching regions with only horizontal lines are ground by parts of grinding wheel 30 except the R-part 30KM.

In the first process [1] as shown in FIG. 6(A), moving backward in oblique direction of X-axis, the grinding wheel 30 removes the grinding allowance [1(0)] of the end face for rough grinding of the end face. In the first process [1], the end face is ground not by the R-part 30KM but by the side surface 30SM and the back taper surface 30BM of the grinding wheel 30.

Next, the second process [2] takes place, see FIG. 6(B). The second process [2] is separated to two steps which are finish grinding step of the end face [2 a] and rough grinding step of cylindrical part [2 b]. In the step [2 a], the grinding wheel 30 moves forward along X-axis (perpendicular to C-axis) and removes grinding allowance [2 a(1)] for finish grinding of the end face. In the step [2 a], the end face is ground by a few regions of the R-part 30KM corresponding to the grinding allowance. Further moving forward along X-axis, the grinding wheel 30 reaches the cylindrical part of the workpiece W and the step [2 b] begins. In the step [2 b], continuously moving forward, the R-part 30KM removes the grinding allowance [2 b(1)], and the external surface 30FM removes the grinding allowance [2 b(0)] for rough grinding of the cylindrical part. Thus the R-part 30KM and the external surface perform. The finish grinding of the cylindrical part may take place in the step [2 b].

As described, the grinding allowances [2 a(1)] and [2 b(1)] are ground by the R-part 30KM of the grinding wheel 30. The R-form is transferred from the R-part 30KM to the region between the end face and the cylindrical part so as the reduce stress concentration.

With referring to FIGS. 1 and 6, the first embodiment will be compared with the prior art about the amount of the grinding allowances removed by the R-part 30KM. The substantial same amount of the grinding allowance is removed in the step [2 b] of the first embodiment and in the step [A1 b] of the prior art by the R-part 30KM.

In the step [2 a] of the first embodiment and in the step [A1 a], the substantial same width of the R-part 30KM performs. Because the allowance width of the prior art is larger than that of the first embodiment at the rotational outward of the workpiece W, the grinding allowance [A1 a(1)] of the prior art is larger than that [2 a(1)] of the first embodiment.

Now, remaining processes (the first process [1] of the first embodiment and the second process [A2] of the prior art) will be compared. In the first process [1] of the first embodiment, the grinding allowance [1(0)] is removed not by the R-part 30KM but by the side surfaces 30SM and the back taper surfaces 30BM. However, in the second process [A2] of the prior art, the R-part 30KM performs.

Therefore, it is clear that the R-part 30KM removes smaller amount of the grinding allowances in the first embodiment than in the prior art. According to the grinding method of the first embodiment, because it is possible to reduce the amount of the grinding allowances removed by the R-part 30KM, the amount of abrasion of the R-part 30KM is reduced. Therefore, the grinding wheel 30 is able to keep its shape at the R-part longer than the prior art so as to gain longer durability.

[Grinding Method of One Cylindrical Part and Two End Faces Sandwiching the Cylindrical Part]

Second embodiment of the invention will be described with reference to FIGS. 7 and 8. The grinding method of the second embodiment is applied to the workpiece W with one cylindrical part and two end faces sandwiching the cylindrical part, for example, crank pins P1 to P4 and adjacent shoulders and/or crank journals J2 to J4 and adjacent shoulders shown in FIG. 8(A). In FIG. 7, hatching regions with horizontal and vertical lines indicate grinding allowances ground by the R-part 30KM of the grinding wheel 30. Hatching regions with only horizontal lines are ground by parts of grinding wheel 30 except the R-part 30KM. Processes [1] to [6] of the second embodiment are shown in FIG. 7.

First and second processes [1] and [2] of the second embodiment are respectively similar to the first and second processes of the first embodiment shown in FIG. 6. In the first process [1], moving backward in oblique direction of X-axis, the grinding wheel 30 removes the grinding allowance [1(0)] of one of the end faces for rough grinding by using the side surface 30SM and the back taper surface 30BM. In the second process [2], moving forward along X-axis (perpendicular to C-axis), the grinding wheel 30 removes the grinding allowances [2 a(1)] and [2 b(1)] by the R-part 30KM and the grinding allowance [2 b(0)] by the external surface 30FM. Thus the grinding wheel 30 grinds the one end face for finish grinding and the cylindrical part for rough grinding. The grinding allowances [1(0)], [2 a(1)], [2 b(1)] and [2 b(0)] are not shown in FIG. 7 but in FIG. 6 because of equivalency.

Third process [3] is a nongrinding stroke. The grinding wheel 30 backwardly moves from C-axis (a little distance away from the cylindrical part), and traverses toward the other end face.

Forth and fifth processes [4] and [5] are substantially the same with the first and second processes [1] and [2]. In fourth process [4], moving backward in oblique direction of X-axis, the grinding wheel 30 removes the grinding allowance of the other end face for rough grinding by using the side surface 30SM and the back taper surface 30BM, as well as the first process [1]. In fifth process [5], moving forward along X-axis (perpendicular to C-axis), the grinding wheel 30 removes the grinding allowances by the R-part 30KM and the grinding allowance by the external surface 30FM, as well as the second process [2]. Thus the grinding wheel 30 grinds the other end face for finish grinding and the cylindrical part for rough grinding.

Finally, in sixth process [6], traversing from the other end face to the one end face in parallel direction of C-axis, the grinding wheel 30 grinds the cylindrical part by using the external surface 30FM for finish grinding.

As described, in the second embodiment, check-like hatching regions in FIG. 7 indicate grinding allowances ground by the R-part 30KM of the grinding wheel 30. In consideration of the check-like hatched grinding allowances ground by the R-part 30KM at the middle of the cylindrical part between both end faces, the grinding allowance [2 b(2)] of the second embodiment in FIG. 7 is substantially as large as that [A1 b(2)] of the prior art in FIG. 2. Thus, as well as comparison between the first embodiment in FIG. 6 and the prior art in FIG. 1, remaining check-like hatched grinding allowances of the second embodiment is smaller than that of the prior art. Compared to the prior art, the second embodiment is able to reduce the amount of the grinding allowances removed by the R-part 30KM. Therefore, because the amount of abrasion of the R-part 30KM is reduced, the grinding wheel 30 is able to keep its shape at the R-part longer than the prior art so as to gain longer durability.

[Grinding Method of Only End Face(s)]

Third embodiment of the invention will be described with reference to FIGS. 8(A) and 9. The third embodiment is applied to the case that grinding is unnecessary to the crank journal J3 but is necessary to the neighboring end faces T3L and T3R. Specifically, respective fillet parts between the cylindrical part J3 and the end faces T3L, T3R are previously processed by a fillet roller so as to become concavities. In such case, it is usual that the cylindrical part J3 is ground by another grinding machine. (The third embodiment omits the explanation of grinding the cylindrical part).

The end face T3L is ground by the processes [1] and [2] of the second embodiment shown in FIG. 7, and similarly the end face T3R is ground by the processes [4] and [5]. Finish grinding is done by the processes [1], [2], [4] and [5]. By the way, because the concavities reduce stress concentration, it is unnecessary to transfer the R-form from the R-parts 30KM of the grinding wheel 30 to the end faces T3L and T3R. Thus it is unnecessary for the grinding wheel 30 to have the R-parts 30KM so that right angle may be applied to the boundaries between the external surface 30FM and the side surfaces 30SM.

According to the above described embodiments, the grinding machine 1 moves the grinding wheel 30 to/away from the workpiece W along X-axis, as shown in FIGS. 3 and 4. However, because relative movement is needed between the grinding wheel 30 and the workpiece W along X-axis, the workpieces W may move to/away from the grinding wheel 30 along X-axis.

Similarly, although the workpiece W moves along Z-axis in the embodiments, the grinding wheel 30 may move along Z-axis. Thus the grinding wheel 30 relatively moves to the workpiece W along Z-axis.

Obviously, numerous modifications and variations of the present invention are possible in light of the above teachings. It is thereby to be understood that within the scope of the appended claims, the present invention may be practiced otherwise than as specifically described herein. 

1. A grinding method of a rotating workpiece having a cylindrical part and at least one end face beside the cylindrical part with a rotating grinding wheel which relatively moves to the workpiece, wherein the grinding wheel has a rotational axis parallel to a rotational axis of the workpiece and has an external surface parallel to its rotational axis, at least one side surface perpendicular to its rotational axis and at least one R-part between the external surface and the side surface, the grinding method comprises processes of: setting the grinding wheel close to the end face of the workpiece and moving the grinding wheel backward in oblique direction to the end face to grind the end face for rough grinding by the side surface; and moving the grinding wheel forward perpendicular to the rotational axis of the workpiece to grind the end face for finish grinding by the R-part and to grind the cylindrical part for rough grinding by the R-part and the external surface.
 2. The grinding method according to claim 1, wherein the grinding wheel inwardly has a back taper surface connected with the side surface, and wherein the back taper surface is used for the rough grinding of the end face.
 3. A grinding method of a rotating workpiece having a cylindrical part and two end faces at both sides of the cylindrical part with a rotating grinding wheel which relatively moves to the workpiece, wherein the grinding wheel has a rotational axis parallel to a rotational axis of the workpiece and has an external surface parallel to its rotational axis, two side surfaces perpendicular to its rotational axis and two R-parts between the external surface and the side surfaces, the grinding method comprises processes of: setting the grinding wheel close to one of the end faces of the workpiece and moving the grinding wheel backward in oblique direction to the one end face to grind the one end face for rough grinding by one of the side surfaces; moving the grinding wheel forward perpendicular to the rotational axis of the workpiece to grind the one end face for finish grinding by one of the R-parts and to grind a part of the cylindrical part close to the one end face for rough grinding by the one R-part and the external surface; setting the grinding wheel close to the other end face of the workpiece and moving the grinding wheel backward in oblique direction to the other end face to grind the other end face for rough grinding by the other side surface; moving the grinding wheel forward perpendicular to the rotational axis of the workpiece to grind the other end face for finish grinding by the other R-part and to grind a part of the cylindrical part close to the other end face for rough grinding by the other R-part and the external surface; and moving the grinding wheel parallel to the rotational axis of the workpiece for finish grinding of the cylindrical part by the one R-part and the external surface.
 4. The grinding method according to claim 3, wherein the grinding wheel inwardly has a back taper surface connected with the side surface, and wherein the back taper surface is used for the rough grinding of the end face.
 5. A grinding method of a rotating workpiece having at least one end face with a rotating grinding wheel which relatively moves to the workpiece, wherein the grinding wheel has a rotational axis parallel to a rotational axis of the workpiece and has an external surface parallel to its rotational axis and at least one side surface perpendicular to its rotational axis, the grinding method comprises processes of: setting the grinding wheel close to the end face of the workpiece and moving the grinding wheel backward in oblique direction to the end face to grind the end face for rough grinding by the side surface; and moving the grinding wheel forward perpendicular to the rotational axis of the workpiece to grind the end face for finish grinding by a boundary between the external surface and the side surface.
 6. The grinding method according to claim 5, wherein the grinding wheel inwardly has a back taper surface connected with the side surface, and wherein the back taper surface is used for the rough grinding of the end face. 